MinT - Best Known (198−91, 198, s)-Nets in Base 4

Best Known (198−91, 198, s)-Nets in Base 4

(198−91, 198, 130)-Net over F₄ — Constructive and digital

Digital (107, 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]

(198−91, 198, 186)-Net over F₄ — Digital

Digital (107, 198, 186)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−91, 198, 2502)-Net in Base 4 — Upper bound on s

There is no (107, 198, 2503)-net in base 4, because

1 times m-reduction [i] would yield (107, 197, 2503)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 40605 578963 505756 742255 908369 850212 503274 717274 435354 304225 090944 601020 956962 225010 671128 061092 146199 497840 098950 078384 > 4¹⁹⁷ [i]