MinT - Best Known (195−80, 195, s)-Nets in Base 4

Best Known (195−80, 195, s)-Nets in Base 4

(195−80, 195, 130)-Net over F₄ — Constructive and digital

Digital (115, 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]

(195−80, 195, 263)-Net over F₄ — Digital

Digital (115, 195, 263)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(195−80, 195, 4493)-Net in Base 4 — Upper bound on s

There is no (115, 195, 4494)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2538 845772 267425 275171 573245 689194 436672 404423 092415 643478 048576 720272 661940 938596 105652 299588 543363 131155 820851 185692 > 4¹⁹⁵ [i]