MinT - Best Known (187−81, 187, s)-Nets in Base 4

Best Known (187−81, 187, s)-Nets in Base 4

(187−81, 187, 130)-Net over F₄ — Constructive and digital

Digital (106, 187, 130)-net over F₄, using

t-expansion [i] based on digital (105, 187, 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]

(187−81, 187, 213)-Net over F₄ — Digital

Digital (106, 187, 213)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(187−81, 187, 3280)-Net in Base 4 — Upper bound on s

There is no (106, 187, 3281)-net in base 4, because

1 times m-reduction [i] would yield (106, 186, 3281)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9677 902408 065114 857845 990050 023261 647312 426056 259231 614187 856364 141494 891677 075435 794889 254424 817351 067441 653596 > 4¹⁸⁶ [i]