MinT - Best Known (145, 145+79, s)-Nets in Base 3

Best Known (145, 145+79, s)-Nets in Base 3

(145, 145+79, 162)-Net over F₃ — Constructive and digital

Digital (145, 224, 162)-net over F₃, using

2 times m-reduction [i] based on digital (145, 226, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 113, 81)-net over F₉, using
  - net from sequence [i] based on digital (32, 80)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
      - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(145, 145+79, 296)-Net over F₃ — Digital

Digital (145, 224, 296)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(145, 145+79, 4078)-Net in Base 3 — Upper bound on s

There is no (145, 224, 4079)-net in base 3, because

1 times m-reduction [i] would yield (145, 223, 4079)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25158 238792 716304 513174 444524 720824 998435 400061 080580 496206 441443 917455 612495 684545 352951 692898 471107 422323 > 3²²³ [i]