MinT - Best Known (52, 52+52, s)-Nets in Base 5

Best Known (52, 52+52, s)-Nets in Base 5

(52, 52+52, 82)-Net over F₅ — Constructive and digital

Digital (52, 104, 82)-net over F₅, using

t-expansion [i] based on digital (48, 104, 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]

(52, 52+52, 108)-Net over F₅ — Digital

Digital (52, 104, 108)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+52, 1629)-Net in Base 5 — Upper bound on s

There is no (52, 104, 1630)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4 956125 078697 299480 416277 710507 918489 531416 761014 663480 035251 738273 152385 > 5¹⁰⁴ [i]