MinT - Best Known (65, 65+72, s)-Nets in Base 5

Best Known (65, 65+72, s)-Nets in Base 5

(65, 65+72, 82)-Net over F₅ — Constructive and digital

Digital (65, 137, 82)-net over F₅, using

t-expansion [i] based on digital (48, 137, 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]

(65, 65+72, 120)-Net over F₅ — Digital

Digital (65, 137, 120)-net over F₅, using

t-expansion [i] based on digital (61, 137, 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]

(65, 65+72, 1605)-Net in Base 5 — Upper bound on s

There is no (65, 137, 1606)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 581941 735359 721582 363082 045067 715893 571210 704378 693001 313577 688926 803305 755006 294325 970361 717825 > 5¹³⁷ [i]