MinT - Best Known (102−85, 102, s)-Nets in Base 32

Best Known (102−85, 102, s)-Nets in Base 32

(102−85, 102, 120)-Net over F₃₂ — Constructive and digital

Digital (17, 102, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 102, 120)-net over F₃₂, using
- net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]

(102−85, 102, 158)-Net over F₃₂ — Digital

Digital (17, 102, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 102, 158)-net over F₃₂, using
- net from sequence [i] based on digital (15, 157)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 15 and N(F) ≥ 158, using
    - an algebraic function field by Beelen and Pellikaan [i]

(102−85, 102, 2196)-Net in Base 32 — Upper bound on s

There is no (17, 102, 2197)-net in base 32, because

1 times m-reduction [i] would yield (17, 101, 2197)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 106 303760 648552 799256 228597 583495 342249 757112 871703 520026 541562 359543 987502 078157 583218 889018 396542 557283 924400 040285 128698 855049 233085 174842 917898 142512 > 32¹⁰¹ [i]