MinT - Best Known (130−107, 130, s)-Nets in Base 16

Best Known (130−107, 130, s)-Nets in Base 16

(130−107, 130, 65)-Net over F₁₆ — Constructive and digital

Digital (23, 130, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 130, 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]

(130−107, 130, 129)-Net over F₁₆ — Digital

Digital (23, 130, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 130, 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]

(130−107, 130, 1141)-Net in Base 16 — Upper bound on s

There is no (23, 130, 1142)-net in base 16, because

1 times m-reduction [i] would yield (23, 129, 1142)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 219952 534884 193151 937861 373028 181775 329418 336479 175081 881668 396347 530605 029066 173814 556207 423516 097732 782419 823486 588258 889083 078020 544099 540359 054243 431541 > 16¹²⁹ [i]