MinT - Best Known (182−75, 182, s)-Nets in Base 4

Best Known (182−75, 182, s)-Nets in Base 4

(182−75, 182, 130)-Net over F₄ — Constructive and digital

Digital (107, 182, 130)-net over F₄, using

t-expansion [i] based on digital (105, 182, 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]

(182−75, 182, 244)-Net over F₄ — Digital

Digital (107, 182, 244)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(182−75, 182, 4275)-Net in Base 4 — Upper bound on s

There is no (107, 182, 4276)-net in base 4, because

1 times m-reduction [i] would yield (107, 181, 4276)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9 471693 308016 337720 747525 204146 962316 614142 686399 882751 694097 742585 969092 213644 908671 626345 429478 099839 063132 > 4¹⁸¹ [i]