MinT - Best Known (60, 60+61, s)-Nets in Base 5

Best Known (60, 60+61, s)-Nets in Base 5

(60, 60+61, 82)-Net over F₅ — Constructive and digital

Digital (60, 121, 82)-net over F₅, using

t-expansion [i] based on digital (48, 121, 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]

(60, 60+61, 118)-Net over F₅ — Digital

Digital (60, 121, 118)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 60+61, 1860)-Net in Base 5 — Upper bound on s

There is no (60, 121, 1861)-net in base 5, because

1 times m-reduction [i] would yield (60, 120, 1861)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 763863 469561 876972 947108 065852 481801 209194 374710 843548 531492 418833 320221 746805 165353 > 5¹²⁰ [i]