MinT - Best Known (82, 82+46, s)-Nets in Base 5

Best Known (82, 82+46, s)-Nets in Base 5

(82, 82+46, 252)-Net over F₅ — Constructive and digital

Digital (82, 128, 252)-net over F₅, using

16 times m-reduction [i] based on digital (82, 144, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 72, 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]

(82, 82+46, 423)-Net over F₅ — Digital

Digital (82, 128, 423)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+46, 18277)-Net in Base 5 — Upper bound on s

There is no (82, 128, 18278)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 294029 820214 700570 194588 756472 287178 728474 913162 600095 249554 818849 773056 317455 076500 612025 > 5¹²⁸ [i]