MinT - Best Known (259−155, 259, s)-Nets in Base 4

Best Known (259−155, 259, s)-Nets in Base 4

(259−155, 259, 104)-Net over F₄ — Constructive and digital

Digital (104, 259, 104)-net over F₄, using

t-expansion [i] based on digital (73, 259, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(259−155, 259, 144)-Net over F₄ — Digital

Digital (104, 259, 144)-net over F₄, using

t-expansion [i] based on digital (91, 259, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(259−155, 259, 960)-Net in Base 4 — Upper bound on s

There is no (104, 259, 961)-net in base 4, because

1 times m-reduction [i] would yield (104, 258, 961)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 220538 453462 865129 191183 502816 614747 289318 455010 960966 325195 046579 989685 943442 662450 618312 149933 398514 377585 027508 632376 157889 876969 550412 620844 039270 756352 > 4²⁵⁸ [i]