MinT - Best Known (72, 72+90, s)-Nets in Base 3

Best Known (72, 72+90, s)-Nets in Base 3

(72, 72+90, 48)-Net over F₃ — Constructive and digital

Digital (72, 162, 48)-net over F₃, using

t-expansion [i] based on digital (45, 162, 48)-net over F₃, using
- net from sequence [i] based on digital (45, 47)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
    - an explicitly constructive algebraic function field [i]

(72, 72+90, 84)-Net over F₃ — Digital

Digital (72, 162, 84)-net over F₃, using

t-expansion [i] based on digital (71, 162, 84)-net over F₃, using
- net from sequence [i] based on digital (71, 83)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 71 and N(F) ≥ 84, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(72, 72+90, 417)-Net in Base 3 — Upper bound on s

There is no (72, 162, 418)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 212072 338679 047120 653447 703845 522232 522267 661432 583074 247487 780703 143168 622925 > 3¹⁶² [i]