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

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

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

Digital (64, 128, 82)-net over F₅, using

t-expansion [i] based on digital (48, 128, 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+64, 127)-Net over F₅ — Digital

Digital (64, 128, 127)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+64, 1975)-Net in Base 5 — Upper bound on s

There is no (64, 128, 1976)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 298229 109739 771508 328763 123948 515990 040240 797990 576974 282088 794856 696566 167344 644840 321025 > 5¹²⁸ [i]