MinT - Best Known (54, 95, s)-Nets in Base 32

Best Known (54, 95, s)-Nets in Base 32

(54, 95, 294)-Net over F₃₂ — Constructive and digital

Digital (54, 95, 294)-net over F₃₂, using

generalized (u,Â u+v)-construction [i] based on
1. digital (7, 20, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]
2. digital (7, 27, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)
3. digital (7, 48, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(54, 95, 513)-Net in Base 32 — Constructive

(54, 95, 513)-net in base 32, using

t-expansion [i] based on (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]

(54, 95, 1931)-Net over F₃₂ — Digital

Digital (54, 95, 1931)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 95, 3177957)-Net in Base 32 — Upper bound on s

There is no (54, 95, 3177958)-net in base 32, because

1 times m-reduction [i] would yield (54, 94, 3177958)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3048 597248 607015 781142 187887 269359 156210 909680 464815 264402 467162 494352 152152 681827 175814 291895 101034 967483 584827 254182 352149 817757 443039 290698 > 32⁹⁴ [i]