MinT - Best Known (258−158, 258, s)-Nets in Base 4

Best Known (258−158, 258, s)-Nets in Base 4

(258−158, 258, 104)-Net over F₄ — Constructive and digital

Digital (100, 258, 104)-net over F₄, using

t-expansion [i] based on digital (73, 258, 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]

(258−158, 258, 144)-Net over F₄ — Digital

Digital (100, 258, 144)-net over F₄, using

t-expansion [i] based on digital (91, 258, 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]

(258−158, 258, 868)-Net in Base 4 — Upper bound on s

There is no (100, 258, 869)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 223201 667845 230822 077537 865536 532676 713673 472154 824689 727830 048540 429627 982253 725903 411250 449348 141902 531438 399133 793553 563761 137382 713368 621072 261713 403424 > 4²⁵⁸ [i]