MinT - Best Known (76, 149, s)-Nets in Base 5

Best Known (76, 149, s)-Nets in Base 5

(76, 149, 98)-Net over F₅ — Constructive and digital

Digital (76, 149, 98)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (9, 45, 26)-net over F₅, using
  - net from sequence [i] based on digital (9, 25)-sequence over F₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 9 and N(F) ≥ 26, using
      - an explicitly constructive algebraic function field [i]
2. digital (31, 104, 72)-net over F₅, using
  - net from sequence [i] based on digital (31, 71)-sequence over F₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 31 and N(F) ≥ 72, using
      - an explicitly constructive algebraic function field [i]

(76, 149, 155)-Net over F₅ — Digital

Digital (76, 149, 155)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(76, 149, 2641)-Net in Base 5 — Upper bound on s

There is no (76, 149, 2642)-net in base 5, because

1 times m-reduction [i] would yield (76, 148, 2642)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 28 099330 153449 164109 542574 294432 383798 993618 777144 208115 049596 294217 397828 635174 684322 398032 520255 411265 > 5¹⁴⁸ [i]