MinT - Best Known (65, 65+66, s)-Nets in Base 5

Best Known (65, 65+66, s)-Nets in Base 5

(65, 65+66, 82)-Net over F₅ — Constructive and digital

Digital (65, 131, 82)-net over F₅, using

t-expansion [i] based on digital (48, 131, 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+66, 126)-Net over F₅ — Digital

Digital (65, 131, 126)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+66, 1934)-Net in Base 5 — Upper bound on s

There is no (65, 131, 1935)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 36 938455 103640 984798 366958 501886 643161 725911 073917 865102 291789 945837 718503 155420 705861 737917 > 5¹³¹ [i]