MinT - Best Known (180, 180+63, s)-Nets in Base 3

Best Known (180, 180+63, s)-Nets in Base 3

(180, 180+63, 324)-Net over F₃ — Constructive and digital

Digital (180, 243, 324)-net over F₃, using

trace code for nets [i] based on digital (18, 81, 108)-net over F₂₇, using
- net from sequence [i] based on digital (18, 107)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 18 and N(F) ≥ 108, using
    - F₃ from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F₂₇ [i]

(180, 180+63, 869)-Net over F₃ — Digital

Digital (180, 243, 869)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(180, 180+63, 32902)-Net in Base 3 — Upper bound on s

There is no (180, 243, 32903)-net in base 3, because

1 times m-reduction [i] would yield (180, 242, 32903)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29 085584 306522 993980 422370 360568 308078 187581 662817 602490 272324 537090 083398 810341 948686 546858 576815 706628 307765 570275 > 3²⁴² [i]