MinT - Best Known (258−146, 258, s)-Nets in Base 4

Best Known (258−146, 258, s)-Nets in Base 4

(258−146, 258, 130)-Net over F₄ — Constructive and digital

Digital (112, 258, 130)-net over F₄, using

t-expansion [i] based on digital (105, 258, 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]

(258−146, 258, 165)-Net over F₄ — Digital

Digital (112, 258, 165)-net over F₄, using

t-expansion [i] based on digital (109, 258, 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]

(258−146, 258, 1193)-Net in Base 4 — Upper bound on s

There is no (112, 258, 1194)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 216941 622245 770310 552785 141916 423466 899932 610635 428603 268012 164919 234445 202392 965233 446830 763964 689405 159751 626008 313792 138665 814680 916898 438800 471060 884774 > 4²⁵⁸ [i]