MinT - Best Known (240−111, 240, s)-Nets in Base 4

Best Known (240−111, 240, s)-Nets in Base 4

(240−111, 240, 130)-Net over F₄ — Constructive and digital

Digital (129, 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]

(240−111, 240, 216)-Net over F₄ — Digital

Digital (129, 240, 216)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(240−111, 240, 2894)-Net in Base 4 — Upper bound on s

There is no (129, 240, 2895)-net in base 4, because

1 times m-reduction [i] would yield (129, 239, 2895)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 790033 712095 261048 054882 935894 614459 405132 685429 831708 680436 502079 244497 638659 494411 077523 456111 422277 376881 041864 323702 297238 480401 523330 264048 > 4²³⁹ [i]