MinT - Best Known (110, 110+137, s)-Nets in Base 4

Best Known (110, 110+137, s)-Nets in Base 4

(110, 110+137, 130)-Net over F₄ — Constructive and digital

Digital (110, 247, 130)-net over F₄, using

t-expansion [i] based on digital (105, 247, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(110, 110+137, 165)-Net over F₄ — Digital

Digital (110, 247, 165)-net over F₄, using

t-expansion [i] based on digital (109, 247, 165)-net over F₄, using
- net from sequence [i] based on digital (109, 164)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
    - Drinfeld modules of rank 1 [i]

(110, 110+137, 1258)-Net in Base 4 — Upper bound on s

There is no (110, 247, 1259)-net in base 4, because

1 times m-reduction [i] would yield (110, 246, 1259)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13193 158854 692258 856579 864816 591015 577358 444659 342451 817722 342572 447107 477749 454080 418203 585384 812182 076439 383953 390350 635805 172645 772964 027157 800026 > 4²⁴⁶ [i]