MinT - Best Known (64, 64+86, s)-Nets in Base 5

Best Known (64, 64+86, s)-Nets in Base 5

(64, 64+86, 82)-Net over F₅ — Constructive and digital

Digital (64, 150, 82)-net over F₅, using

t-expansion [i] based on digital (48, 150, 82)-net over F₅, using
- net from sequence [i] based on digital (48, 81)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 48 and N(F) ≥ 82, using
    - an explicitly constructive algebraic function field [i]

(64, 64+86, 120)-Net over F₅ — Digital

Digital (64, 150, 120)-net over F₅, using

t-expansion [i] based on digital (61, 150, 120)-net over F₅, using
- net from sequence [i] based on digital (61, 119)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 61 and N(F) ≥ 120, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(64, 64+86, 1126)-Net in Base 5 — Upper bound on s

There is no (64, 150, 1127)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 714 598636 595793 266480 464078 936097 313191 579404 237707 367046 657958 799769 694853 131204 141943 205561 153683 531125 > 5¹⁵⁰ [i]