MinT - Best Known (198−79, 198, s)-Nets in Base 4

Best Known (198−79, 198, s)-Nets in Base 4

(198−79, 198, 130)-Net over F₄ — Constructive and digital

Digital (119, 198, 130)-net over F₄, using

t-expansion [i] based on digital (105, 198, 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]

(198−79, 198, 292)-Net over F₄ — Digital

Digital (119, 198, 292)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−79, 198, 5610)-Net in Base 4 — Upper bound on s

There is no (119, 198, 5611)-net in base 4, because

1 times m-reduction [i] would yield (119, 197, 5611)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 40441 531130 405594 784701 919244 188488 139810 751193 463629 691471 451095 046181 154169 807844 541858 596134 782544 526748 483946 473568 > 4¹⁹⁷ [i]