MinT - Best Known (246−153, 246, s)-Nets in Base 4

Best Known (246−153, 246, s)-Nets in Base 4

(246−153, 246, 104)-Net over F₄ — Constructive and digital

Digital (93, 246, 104)-net over F₄, using

t-expansion [i] based on digital (73, 246, 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]

(246−153, 246, 144)-Net over F₄ — Digital

Digital (93, 246, 144)-net over F₄, using

t-expansion [i] based on digital (91, 246, 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]

(246−153, 246, 785)-Net in Base 4 — Upper bound on s

There is no (93, 246, 786)-net in base 4, because

1 times m-reduction [i] would yield (93, 245, 786)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3233 508540 402198 063925 536834 284307 007232 445671 137519 561590 982263 511337 648853 196134 999165 422280 230607 134879 589307 770418 379388 534088 067594 389164 286192 > 4²⁴⁵ [i]