MinT - Best Known (252−117, 252, s)-Nets in Base 4

Best Known (252−117, 252, s)-Nets in Base 4

(252−117, 252, 130)-Net over F₄ — Constructive and digital

Digital (135, 252, 130)-net over F₄, using

t-expansion [i] based on digital (105, 252, 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]

(252−117, 252, 223)-Net over F₄ — Digital

Digital (135, 252, 223)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(252−117, 252, 2969)-Net in Base 4 — Upper bound on s

There is no (135, 252, 2970)-net in base 4, because

1 times m-reduction [i] would yield (135, 251, 2970)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13 236907 786922 880371 357408 131845 508546 946427 759757 816705 991360 532969 551804 980235 579214 449804 016092 879669 668908 975853 483739 592941 333794 445080 092961 705120 > 4²⁵¹ [i]