MinT - Best Known (244−147, 244, s)-Nets in Base 4

Best Known (244−147, 244, s)-Nets in Base 4

(244−147, 244, 104)-Net over F₄ — Constructive and digital

Digital (97, 244, 104)-net over F₄, using

t-expansion [i] based on digital (73, 244, 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]

(244−147, 244, 144)-Net over F₄ — Digital

Digital (97, 244, 144)-net over F₄, using

t-expansion [i] based on digital (91, 244, 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]

(244−147, 244, 883)-Net in Base 4 — Upper bound on s

There is no (97, 244, 884)-net in base 4, because

1 times m-reduction [i] would yield (97, 243, 884)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 206 915434 245768 855376 033733 097756 390298 676982 601780 332991 359348 208434 394083 522643 311905 022133 075483 225884 396148 623532 155837 128905 555863 151560 726718 > 4²⁴³ [i]