MinT - Best Known (260−167, 260, s)-Nets in Base 4

Best Known (260−167, 260, s)-Nets in Base 4

(260−167, 260, 104)-Net over F₄ — Constructive and digital

Digital (93, 260, 104)-net over F₄, using

t-expansion [i] based on digital (73, 260, 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]

(260−167, 260, 144)-Net over F₄ — Digital

Digital (93, 260, 144)-net over F₄, using

t-expansion [i] based on digital (91, 260, 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]

(260−167, 260, 732)-Net in Base 4 — Upper bound on s

There is no (93, 260, 733)-net in base 4, because

1 times m-reduction [i] would yield (93, 259, 733)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 870041 381079 166131 114842 522310 804648 123726 668289 740890 793701 612968 083232 511008 565142 622769 783686 920872 082555 908780 070039 109500 604094 564543 115462 016534 359740 > 4²⁵⁹ [i]