MinT - Best Known (100−51, 100, s)-Nets in Base 32

Best Known (100−51, 100, s)-Nets in Base 32

(100−51, 100, 240)-Net over F₃₂ — Constructive and digital

Digital (49, 100, 240)-net over F₃₂, using

3 times m-reduction [i] based on digital (49, 103, 240)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 38, 120)-net over F₃₂, using
    - net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
        a function field by SÃ©mirat [i]
  2. digital (11, 65, 120)-net over F₃₂, using
    - net from sequence [i] based on digital (11, 119)-sequence over F₃₂ (see above)

(100−51, 100, 513)-Net in Base 32 — Constructive

(49, 100, 513)-net in base 32, using

t-expansion [i] based on (46, 100, 513)-net in base 32, using
- 8 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
  - base change [i] based on digital (28, 90, 513)-net over F₆₄, using
    - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
        the Hermitian function field over F₆₄ [i]

(100−51, 100, 656)-Net over F₃₂ — Digital

Digital (49, 100, 656)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(100−51, 100, 299667)-Net in Base 32 — Upper bound on s

There is no (49, 100, 299668)-net in base 32, because

1 times m-reduction [i] would yield (49, 99, 299668)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 102298 644939 806033 542388 847566 588982 581985 359458 710193 465504 519800 023897 250355 845577 321119 881456 979786 635707 312071 718520 198238 586421 458463 446299 673168 > 32⁹⁹ [i]