MinT - Best Known (252−153, 252, s)-Nets in Base 4

Best Known (252−153, 252, s)-Nets in Base 4

(252−153, 252, 104)-Net over F₄ — Constructive and digital

Digital (99, 252, 104)-net over F₄, using

t-expansion [i] based on digital (73, 252, 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]

(252−153, 252, 144)-Net over F₄ — Digital

Digital (99, 252, 144)-net over F₄, using

t-expansion [i] based on digital (91, 252, 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]

(252−153, 252, 883)-Net in Base 4 — Upper bound on s

There is no (99, 252, 884)-net in base 4, because

1 times m-reduction [i] would yield (99, 251, 884)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13 454270 874152 265121 410192 697681 675156 583363 176177 462169 813438 181281 493954 615425 236031 742724 517736 111903 215579 909682 546973 489985 884273 151987 106310 672852 > 4²⁵¹ [i]