MinT - Best Known (187−73, 187, s)-Nets in Base 4

Best Known (187−73, 187, s)-Nets in Base 4

(187−73, 187, 130)-Net over F₄ — Constructive and digital

Digital (114, 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]

(187−73, 187, 299)-Net over F₄ — Digital

Digital (114, 187, 299)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(187−73, 187, 6111)-Net in Base 4 — Upper bound on s

There is no (114, 187, 6112)-net in base 4, because

1 times m-reduction [i] would yield (114, 186, 6112)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9628 804453 820320 358562 197407 209020 839586 698331 704499 069191 867599 003692 894958 286881 133634 115244 964929 819411 079446 > 4¹⁸⁶ [i]