MinT - Best Known (223−109, 223, s)-Nets in Base 4

Best Known (223−109, 223, s)-Nets in Base 4

(223−109, 223, 130)-Net over F₄ — Constructive and digital

Digital (114, 223, 130)-net over F₄, using

t-expansion [i] based on digital (105, 223, 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]

(223−109, 223, 170)-Net over F₄ — Digital

Digital (114, 223, 170)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(223−109, 223, 2043)-Net in Base 4 — Upper bound on s

There is no (114, 223, 2044)-net in base 4, because

1 times m-reduction [i] would yield (114, 222, 2044)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 46 586961 988840 204506 018701 005090 450812 749617 633344 837984 396895 709062 001422 688846 971370 942031 338955 967967 519077 151946 740353 910586 878830 > 4²²² [i]