MinT - Best Known (222−105, 222, s)-Nets in Base 4

Best Known (222−105, 222, s)-Nets in Base 4

(222−105, 222, 130)-Net over F₄ — Constructive and digital

Digital (117, 222, 130)-net over F₄, using

t-expansion [i] based on digital (105, 222, 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]

(222−105, 222, 188)-Net over F₄ — Digital

Digital (117, 222, 188)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(222−105, 222, 2398)-Net in Base 4 — Upper bound on s

There is no (117, 222, 2399)-net in base 4, because

1 times m-reduction [i] would yield (117, 221, 2399)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 541323 537159 488277 523562 928003 112061 026983 277547 343532 390791 540390 913182 894963 702205 538748 969156 286929 483668 056759 742524 212163 071470 > 4²²¹ [i]