MinT - Best Known (198−92, 198, s)-Nets in Base 4

Best Known (198−92, 198, s)-Nets in Base 4

(198−92, 198, 130)-Net over F₄ — Constructive and digital

Digital (106, 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]

(198−92, 198, 179)-Net over F₄ — Digital

Digital (106, 198, 179)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−92, 198, 2304)-Net in Base 4 — Upper bound on s

There is no (106, 198, 2305)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 163355 626597 526893 982756 256562 244816 856186 253984 354849 167068 382297 702463 568262 845802 509072 507778 158339 500036 668784 489600 > 4¹⁹⁸ [i]