MinT - Best Known (112, 255, s)-Nets in Base 4

Best Known (112, 255, s)-Nets in Base 4

(112, 255, 130)-Net over F₄ — Constructive and digital

Digital (112, 255, 130)-net over F₄, using

t-expansion [i] based on digital (105, 255, 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]

(112, 255, 165)-Net over F₄ — Digital

Digital (112, 255, 165)-net over F₄, using

t-expansion [i] based on digital (109, 255, 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]

(112, 255, 1237)-Net in Base 4 — Upper bound on s

There is no (112, 255, 1238)-net in base 4, because

1 times m-reduction [i] would yield (112, 254, 1238)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 857 431363 408138 024777 896894 615528 678291 024109 574514 103442 126715 187679 105159 065052 484709 070340 918621 797009 683701 121437 485977 045983 576328 552135 009413 436840 > 4²⁵⁴ [i]