MinT - Best Known (76−65, 76, s)-Nets in Base 128

Best Known (76−65, 76, s)-Nets in Base 128

(76−65, 76, 288)-Net over F₁₂₈ — Constructive and digital

Digital (11, 76, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 76, 288)-net over F₁₂₈, using
- net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
    - a function field by SÃ©mirat [i]

(76−65, 76, 296)-Net over F₁₂₈ — Digital

Digital (11, 76, 296)-net over F₁₂₈, using

t-expansion [i] based on digital (10, 76, 296)-net over F₁₂₈, using
- net from sequence [i] based on digital (10, 295)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 10 and N(F) ≥ 296, using
    - a curve from the manYPoints database [i]

(76−65, 76, 8731)-Net in Base 128 — Upper bound on s

There is no (11, 76, 8732)-net in base 128, because

1 times m-reduction [i] would yield (11, 75, 8732)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 110 211169 179677 966194 424964 035568 377698 660510 275263 809105 967427 269118 045545 847266 061348 604470 814662 561172 543766 767422 798718 914927 058603 546320 764659 527607 914640 > 128⁷⁵ [i]