MinT - Best Known (212−87, 212, s)-Nets in Base 4

Best Known (212−87, 212, s)-Nets in Base 4

(212−87, 212, 130)-Net over F₄ — Constructive and digital

Digital (125, 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]

(212−87, 212, 283)-Net over F₄ — Digital

Digital (125, 212, 283)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(212−87, 212, 5030)-Net in Base 4 — Upper bound on s

There is no (125, 212, 5031)-net in base 4, because

1 times m-reduction [i] would yield (125, 211, 5031)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 878080 171193 358487 591632 777384 566956 179602 009038 607470 457664 221337 974206 947673 386091 735705 269433 459133 397827 820481 066026 297984 > 4²¹¹ [i]