MinT - Best Known (99−83, 99, s)-Nets in Base 16

Best Known (99−83, 99, s)-Nets in Base 16

(99−83, 99, 65)-Net over F₁₆ — Constructive and digital

Digital (16, 99, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 99, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(99−83, 99, 98)-Net over F₁₆ — Digital

Digital (16, 99, 98)-net over F₁₆, using

t-expansion [i] based on digital (15, 99, 98)-net over F₁₆, using
- net from sequence [i] based on digital (15, 97)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 15 and N(F) ≥ 98, using
    - a curve from the manYPoints database [i]

(99−83, 99, 790)-Net in Base 16 — Upper bound on s

There is no (16, 99, 791)-net in base 16, because

1 times m-reduction [i] would yield (16, 98, 791)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 10511 275023 909652 425602 696138 614297 803204 268682 902592 094350 581206 561599 484236 393721 626776 220534 906401 126304 576568 637216 > 16⁹⁸ [i]