MinT - Best Known (71, 71+63, s)-Nets in Base 5

Best Known (71, 71+63, s)-Nets in Base 5

(71, 71+63, 132)-Net over F₅ — Constructive and digital

Digital (71, 134, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 67, 66)-net over F₂₅, using
- net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
    - a function field by GarcÃa and Quoos [i]

(71, 71+63, 163)-Net over F₅ — Digital

Digital (71, 134, 163)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 71+63, 3073)-Net in Base 5 — Upper bound on s

There is no (71, 134, 3074)-net in base 5, because

1 times m-reduction [i] would yield (71, 133, 3074)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 926 124299 432106 929025 441188 196873 256781 349973 446940 183240 840068 051909 916373 903344 033488 256041 > 5¹³³ [i]