MinT - Best Known (84, 84+53, s)-Nets in Base 5

Best Known (84, 84+53, s)-Nets in Base 5

(84, 84+53, 252)-Net over F₅ — Constructive and digital

Digital (84, 137, 252)-net over F₅, using

11 times m-reduction [i] based on digital (84, 148, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 74, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(84, 84+53, 335)-Net over F₅ — Digital

Digital (84, 137, 335)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 84+53, 11931)-Net in Base 5 — Upper bound on s

There is no (84, 137, 11932)-net in base 5, because

1 times m-reduction [i] would yield (84, 136, 11932)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 114931 985447 509634 310396 459956 230677 102150 112983 430280 416716 228232 233771 378216 876919 778095 757377 > 5¹³⁶ [i]