MinT - Best Known (113, 113+143, s)-Nets in Base 4

Best Known (113, 113+143, s)-Nets in Base 4

(113, 113+143, 130)-Net over F₄ — Constructive and digital

Digital (113, 256, 130)-net over F₄, using

t-expansion [i] based on digital (105, 256, 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]

(113, 113+143, 165)-Net over F₄ — Digital

Digital (113, 256, 165)-net over F₄, using

t-expansion [i] based on digital (109, 256, 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]

(113, 113+143, 1263)-Net in Base 4 — Upper bound on s

There is no (113, 256, 1264)-net in base 4, because

1 times m-reduction [i] would yield (113, 255, 1264)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3517 818669 548717 930532 022866 023424 058998 547198 176283 708757 374713 974894 306881 993144 532381 312856 238267 456969 643243 080652 372878 673591 330649 633147 534910 024933 > 4²⁵⁵ [i]