MinT - Best Known (212−90, 212, s)-Nets in Base 4

Best Known (212−90, 212, s)-Nets in Base 4

(212−90, 212, 130)-Net over F₄ — Constructive and digital

Digital (122, 212, 130)-net over F₄, using

t-expansion [i] based on digital (105, 212, 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]

(212−90, 212, 254)-Net over F₄ — Digital

Digital (122, 212, 254)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(212−90, 212, 3994)-Net in Base 4 — Upper bound on s

There is no (122, 212, 3995)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 43 695922 180070 539442 271593 642102 787371 361793 970711 504686 311291 967115 918835 094252 288713 135534 787005 486304 811593 129137 753501 561184 > 4²¹² [i]