MinT - Best Known (104−88, 104, s)-Nets in Base 16

Best Known (104−88, 104, s)-Nets in Base 16

(104−88, 104, 65)-Net over F₁₆ — Constructive and digital

Digital (16, 104, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 104, 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]

(104−88, 104, 98)-Net over F₁₆ — Digital

Digital (16, 104, 98)-net over F₁₆, using

t-expansion [i] based on digital (15, 104, 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]

(104−88, 104, 782)-Net in Base 16 — Upper bound on s

There is no (16, 104, 783)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 170534 050402 264201 245953 867823 738008 822752 090811 114553 640430 323547 591952 398857 286461 008545 053434 457517 556791 139548 598405 711256 > 16¹⁰⁴ [i]