MinT - Best Known (195−89, 195, s)-Nets in Base 4

Best Known (195−89, 195, s)-Nets in Base 4

(195−89, 195, 130)-Net over F₄ — Constructive and digital

Digital (106, 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]

(195−89, 195, 187)-Net over F₄ — Digital

Digital (106, 195, 187)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(195−89, 195, 2560)-Net in Base 4 — Upper bound on s

There is no (106, 195, 2561)-net in base 4, because

1 times m-reduction [i] would yield (106, 194, 2561)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 638 732270 868504 254627 392596 163822 998751 417559 484201 480536 259802 373598 873146 191120 243050 132193 990244 342350 915072 673920 > 4¹⁹⁴ [i]