MinT - Best Known (101, 101+89, s)-Nets in Base 4

Best Known (101, 101+89, s)-Nets in Base 4

(101, 101+89, 130)-Net over F₄ — Constructive and digital

Digital (101, 190, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 95, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(101, 101+89, 169)-Net over F₄ — Digital

Digital (101, 190, 169)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(101, 101+89, 2181)-Net in Base 4 — Upper bound on s

There is no (101, 190, 2182)-net in base 4, because

1 times m-reduction [i] would yield (101, 189, 2182)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 617376 582597 500188 907157 155769 895384 899299 957722 414309 757072 425345 437997 328168 776281 400132 202218 248455 935868 065360 > 4¹⁸⁹ [i]