MinT - Best Known (187−77, 187, s)-Nets in Base 4

Best Known (187−77, 187, s)-Nets in Base 4

(187−77, 187, 130)-Net over F₄ — Constructive and digital

Digital (110, 187, 130)-net over F₄, using

t-expansion [i] based on digital (105, 187, 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]

(187−77, 187, 251)-Net over F₄ — Digital

Digital (110, 187, 251)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(187−77, 187, 4400)-Net in Base 4 — Upper bound on s

There is no (110, 187, 4401)-net in base 4, because

1 times m-reduction [i] would yield (110, 186, 4401)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9620 254014 452304 816453 987474 929387 653469 739549 682340 110897 600312 851474 853347 379049 545834 162176 229334 466842 844088 > 4¹⁸⁶ [i]