MinT - Best Known (84−23, 84, s)-Nets in Base 5

Best Known (84−23, 84, s)-Nets in Base 5

(84−23, 84, 296)-Net over F₅ — Constructive and digital

Digital (61, 84, 296)-net over F₅, using

trace code for nets [i] based on digital (19, 42, 148)-net over F₂₅, using
- net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
    - a function field by GarcÃa and Quoos [i]

(84−23, 84, 1067)-Net over F₅ — Digital

Digital (61, 84, 1067)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(84−23, 84, 230667)-Net in Base 5 — Upper bound on s

There is no (61, 84, 230668)-net in base 5, because

1 times m-reduction [i] would yield (61, 83, 230668)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 10340 119051 076574 671695 917968 359377 365435 058120 900650 187569 > 5⁸³ [i]