MinT - Best Known (144−80, 144, s)-Nets in Base 5

Best Known (144−80, 144, s)-Nets in Base 5

(144−80, 144, 82)-Net over F₅ — Constructive and digital

Digital (64, 144, 82)-net over F₅, using

t-expansion [i] based on digital (48, 144, 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]

(144−80, 144, 120)-Net over F₅ — Digital

Digital (64, 144, 120)-net over F₅, using

t-expansion [i] based on digital (61, 144, 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]

(144−80, 144, 1265)-Net in Base 5 — Upper bound on s

There is no (64, 144, 1266)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 46245 987159 384319 804643 076441 581156 654955 023965 107697 006254 902794 680970 292145 660513 360468 595800 535425 > 5¹⁴⁴ [i]