MinT - Best Known (111, 111+75, s)-Nets in Base 4

Best Known (111, 111+75, s)-Nets in Base 4

(111, 111+75, 130)-Net over F₄ — Constructive and digital

Digital (111, 186, 130)-net over F₄, using

t-expansion [i] based on digital (105, 186, 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]

(111, 111+75, 267)-Net over F₄ — Digital

Digital (111, 186, 267)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 111+75, 4971)-Net in Base 4 — Upper bound on s

There is no (111, 186, 4972)-net in base 4, because

1 times m-reduction [i] would yield (111, 185, 4972)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2420 532005 207491 944998 269994 317649 281860 150103 679075 305913 135770 791039 849061 183915 298333 360015 656170 606134 096230 > 4¹⁸⁵ [i]