MinT - Best Known (247−143, 247, s)-Nets in Base 4

Best Known (247−143, 247, s)-Nets in Base 4

(247−143, 247, 104)-Net over F₄ — Constructive and digital

Digital (104, 247, 104)-net over F₄, using

t-expansion [i] based on digital (73, 247, 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]

(247−143, 247, 144)-Net over F₄ — Digital

Digital (104, 247, 144)-net over F₄, using

t-expansion [i] based on digital (91, 247, 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]

(247−143, 247, 1050)-Net in Base 4 — Upper bound on s

There is no (104, 247, 1051)-net in base 4, because

1 times m-reduction [i] would yield (104, 246, 1051)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13260 525719 681788 745129 606962 513678 581530 848216 340668 003786 185555 742731 065553 731124 727279 404426 596070 665946 329648 725134 187693 084537 676657 489186 010112 > 4²⁴⁶ [i]