MinT - Best Known (102, 102+158, s)-Nets in Base 4

Best Known (102, 102+158, s)-Nets in Base 4

(102, 102+158, 104)-Net over F₄ — Constructive and digital

Digital (102, 260, 104)-net over F₄, using

t-expansion [i] based on digital (73, 260, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(102, 102+158, 144)-Net over F₄ — Digital

Digital (102, 260, 144)-net over F₄, using

t-expansion [i] based on digital (91, 260, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(102, 102+158, 901)-Net in Base 4 — Upper bound on s

There is no (102, 260, 902)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 496707 661867 437830 236485 795653 357590 760969 039708 526761 606688 009864 848279 286379 923778 509400 111447 540914 993324 091149 257218 321846 658496 005439 393676 237904 619712 > 4²⁶⁰ [i]