MinT - Best Known (195−85, 195, s)-Nets in Base 4

Best Known (195−85, 195, s)-Nets in Base 4

(195−85, 195, 130)-Net over F₄ — Constructive and digital

Digital (110, 195, 130)-net over F₄, using

t-expansion [i] based on digital (105, 195, 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]

(195−85, 195, 217)-Net over F₄ — Digital

Digital (110, 195, 217)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(195−85, 195, 3289)-Net in Base 4 — Upper bound on s

There is no (110, 195, 3290)-net in base 4, because

1 times m-reduction [i] would yield (110, 194, 3290)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 635 582614 053125 389278 525774 749775 553780 619613 564396 220752 171278 464963 380074 548239 764961 403604 440164 434382 511253 739520 > 4¹⁹⁴ [i]