MinT - Best Known (95−49, 95, s)-Nets in Base 32

Best Known (95−49, 95, s)-Nets in Base 32

(95−49, 95, 240)-Net over F₃₂ — Constructive and digital

Digital (46, 95, 240)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (11, 35, 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, 60, 120)-net over F₃₂, using
  - net from sequence [i] based on digital (11, 119)-sequence over F₃₂ (see above)

(95−49, 95, 513)-Net in Base 32 — Constructive

(46, 95, 513)-net in base 32, using

13 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]

(95−49, 95, 586)-Net over F₃₂ — Digital

Digital (46, 95, 586)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(95−49, 95, 248399)-Net in Base 32 — Upper bound on s

There is no (46, 95, 248400)-net in base 32, because

1 times m-reduction [i] would yield (46, 94, 248400)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3048 794798 804654 323258 851586 627991 072007 892981 093084 223661 861456 768902 684474 781867 286874 278550 282507 955671 144074 798488 497916 062256 422212 459996 > 32⁹⁴ [i]