MinT - Best Known (240−126, 240, s)-Nets in Base 4

Best Known (240−126, 240, s)-Nets in Base 4

(240−126, 240, 130)-Net over F₄ — Constructive and digital

Digital (114, 240, 130)-net over F₄, using

t-expansion [i] based on digital (105, 240, 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]

(240−126, 240, 165)-Net over F₄ — Digital

Digital (114, 240, 165)-net over F₄, using

t-expansion [i] based on digital (109, 240, 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]

(240−126, 240, 1541)-Net in Base 4 — Upper bound on s

There is no (114, 240, 1542)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 215325 972499 668629 494172 069902 786285 983868 266653 226675 183120 836314 562218 485763 066232 189905 403156 737025 062673 389472 199869 812825 531178 707533 640960 > 4²⁴⁰ [i]