MinT - Best Known (115−93, 115, s)-Nets in Base 16

Best Known (115−93, 115, s)-Nets in Base 16

(115−93, 115, 65)-Net over F₁₆ — Constructive and digital

Digital (22, 115, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 115, 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]

(115−93, 115, 129)-Net over F₁₆ — Digital

Digital (22, 115, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 115, 129)-net over F₁₆, using
- net from sequence [i] based on digital (19, 128)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 19 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(115−93, 115, 1131)-Net in Base 16 — Upper bound on s

There is no (22, 115, 1132)-net in base 16, because

1 times m-reduction [i] would yield (22, 114, 1132)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 190699 102602 797842 103186 880279 181891 617267 848447 832058 824946 642728 419362 478017 090851 768516 822362 913931 997066 060135 678578 020508 000142 953456 > 16¹¹⁴ [i]