MinT - Best Known (199−89, 199, s)-Nets in Base 4

Best Known (199−89, 199, s)-Nets in Base 4

(199−89, 199, 130)-Net over F₄ — Constructive and digital

Digital (110, 199, 130)-net over F₄, using

t-expansion [i] based on digital (105, 199, 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]

(199−89, 199, 203)-Net over F₄ — Digital

Digital (110, 199, 203)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(199−89, 199, 2908)-Net in Base 4 — Upper bound on s

There is no (110, 199, 2909)-net in base 4, because

1 times m-reduction [i] would yield (110, 198, 2909)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 161612 043755 480282 902839 150094 970374 869262 058069 086990 685283 096633 105497 097340 687746 179517 826474 624251 490089 818971 139974 > 4¹⁹⁸ [i]